The Constant Geometric Speed Schedule for Adiabatic State Preparation
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866911672533254144 |
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| author | Han, Mancheon Park, Hyowon Choi, Sangkook |
| author_facet | Han, Mancheon Park, Hyowon Choi, Sangkook |
| contents | The efficiency of adiabatic quantum evolution is governed by the evolution time $T$, which typically scales as $\mathcal{O}(Δ^{-2})$ with the minimum energy gap $Δ$. However, the rigorous lower bound is $\mathcal{O}(LΔ^{-1})$, where $L$ is the adiabatic path length. Although $L$ is formally upper-bounded by $\mathcal{O}(Δ^{-1})$, such a bound is often too loose in practice, and $L$ can be bounded independently of $Δ$. This indicates the potential for a quadratic speedup through adiabatic schedule construction. Here, we introduce the constant geometric speed (CGS) schedule, which traverses the adiabatic path at a uniform rate. We show that this approach reduces the scaling of the evolution time by a factor of $Δ^{-1}$, provided $L$ remains bounded independently of $Δ$. We propose a segmented CGS protocol where path segment lengths are computed from eigenstate overlaps on the fly, reducing the prior spectral-knowledge requirement from the full gap function $Δ(s)$ to just a global lower bound on the energy gap. Numerical tests on adiabatic unstructured search, N$_2$, and a [2Fe-2S] cluster demonstrate the optimal $Δ^{-1}$ scaling, confirming a quadratic speedup over the standard linear schedule. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_01923 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Constant Geometric Speed Schedule for Adiabatic State Preparation Han, Mancheon Park, Hyowon Choi, Sangkook Quantum Physics The efficiency of adiabatic quantum evolution is governed by the evolution time $T$, which typically scales as $\mathcal{O}(Δ^{-2})$ with the minimum energy gap $Δ$. However, the rigorous lower bound is $\mathcal{O}(LΔ^{-1})$, where $L$ is the adiabatic path length. Although $L$ is formally upper-bounded by $\mathcal{O}(Δ^{-1})$, such a bound is often too loose in practice, and $L$ can be bounded independently of $Δ$. This indicates the potential for a quadratic speedup through adiabatic schedule construction. Here, we introduce the constant geometric speed (CGS) schedule, which traverses the adiabatic path at a uniform rate. We show that this approach reduces the scaling of the evolution time by a factor of $Δ^{-1}$, provided $L$ remains bounded independently of $Δ$. We propose a segmented CGS protocol where path segment lengths are computed from eigenstate overlaps on the fly, reducing the prior spectral-knowledge requirement from the full gap function $Δ(s)$ to just a global lower bound on the energy gap. Numerical tests on adiabatic unstructured search, N$_2$, and a [2Fe-2S] cluster demonstrate the optimal $Δ^{-1}$ scaling, confirming a quadratic speedup over the standard linear schedule. |
| title | The Constant Geometric Speed Schedule for Adiabatic State Preparation |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2510.01923 |